Thesis (doctoral)--Universität Basel, 1911. / Vita.

Thesis--Copenhagen. / "Fortegnelse over større værker, som gentagne gange citeres": p. [x].

Thesis (M. Sc.)--York University, 1998. Graduate Programme in Chemistry. / Typescript. Includes bibliographical references (leaves 158-169). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL:http://wwwlib.umi.com/cr/yorku/fullcit?pMQ27385.

Thesis--Ph. D., University of Hong Kong, 1982.

Thesis (M. Sc.)--University of Hong Kong, 1970. / Mimeographed.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 100-102).

Thesis (Ph. D.)--University of Hong Kong, 2002. / Includes bibliographical references.

High frequency wave propagation is well described even at caustics by Gaussian beams and the complex eikonal equation. In contrast to the real eikonal equation, the complex eikonal equation is elliptic and not well posed as an initial value problem. We develop a new model that approximates the 2D complex eikonal equation but is well posed as an initial value problem. This model consists of a coupled system of partial and ordinary differential equations. We prove that there exists a local solution to this new system by a Picard iteration method and show uniqueness under certain constraints. Different numerical approximations are then developed based on direct finite difference approximations or the method of characteristics. Numerical simulations with a variety of velocity profiles are presented and compared with solutions to the corresponding Helmholtz equation. / text

published_or_final_version / Mathematics / Master / Master of Philosophy

Wall-bounded turbulent dispersed multiphase flows occur in a variety of industrial, biological and environmental applications. The complex nature of the carrier and the particulate phase is elevated to a higher level when introducing geometrical complexities such as curved walls. Realising such flows and dispersed phases poses challenging problems both from computational and also physical point of view. The present thesis addresses some of these issues by studying a coupled Eulerian–Lagrangian computational framework. The content of the thesis addresses both turbulent wall flows and coupled particle motion. In the first part, turbulent flow in straight pipes is simulated by means of direct numerical simulation (DNS) with the spectrally accurate code nek5000  to examine the Reynolds-number effect on turbulence statistics. The effect of the curvature to these canonical turbulent pipe flows is then added to generate Prandtl’s secondary motion of first kind. These configurations, as primary complex geometries in this study, are examined by means of statistical analysis to unfold the evolution of turbulence characteristics from a straight pipe. A fundamentally different Prandtl’s secondary motion of the second kind is also put to test by adding side-walls to a canonical turbulent channel flow and analysing the evolution of various statistical quantities with varying the duct width-to-height aspect ratios. Having obtained a characterisation of the turbulent flow in the geometries of bent pipes and ducts, the dispersion of small heavy particles is modelled in these configurations by means of point particles which are one-way coupled to the flow. For this purpose a parallel Lagrangian Particle Tracking (LPT) scheme is implemented in the spectral-element code nek5000 . Its numerical accuracy, parallel scalability and general performance in realistic situations is scrutinised. The analysis of the resulting particle fields shows that even a small amount of secondary motion has a profound impact on the particle phase dynamics and its concentration maps. For each of the aforementioned turbulent flow cases new and challenging questions have arisen to be addressed in the present research works. The goal of extending understanding of the particle dispersion in turbulent bent pipes and rectangular ducts are also achieved. / <p>QC 20151118</p>